MATLAB: How to solve a system of three equations with 2 parameters and initial values

ode45parameters

I was able to figure out how to solve the system with using only one parameter. Here are my lines:
clear all
clc
syms t x a 
for a = [0:.25:1];
g = @(t,x,a)[3*(a-1)*x(1)+.01*x(3)-.0005*x(1)*x(2);.0005*x(1)*x(2)-.05*x(2)-.02*x(2);3*a+.05*x(2)-.01*x(3)];
[t,xa] = ode45(@(t,x) g(t,x,a),[0 50],[990 10 0]);
figure
plot(t,xa(:,1),t,xa(:,2),t,xa(:,3))
title(['Viral Spread of Infection'])
xlabel('t (days)')
ylabel('Population')
legend('S','I','R')
end
but now I am wanting to add another parameter "q" so that q = 0:2:10 and
g = [3*(a-1)*x(1)+.01*x(3)-.0005*x(1)*x(2)-q*x(2);.0005*x(1)*x(2)-.05*x(2)-.02*x(2)-q*x(2);3*a+.05*x(2)-.01*x(3)];
I tried just adding q to the same places as a, but it didn't work.
Please help!

Best Answer

I am guessing that I=x(2). (It would be nice to know for sure.)
This is one option:
av = 0 : 0.25 : 1;
qv = 0 : 2 : 10;
for k1 = 1:numel(av)
    for k2 = 1:numel(qv)
        g = @(t,x,a,q)[3*(a-1)*x(1)+.01*x(3)-.0005*x(1)*x(2)-q*x(2);.0005*x(1)*x(2)-.05*x(2)-.02*x(2)-q*x(2);3*a+.05*x(2)-.01*x(3)];
        [t,xa] = ode45(@(t,x) g(t,x,av(k1),qv(k2)),[0 50],[990 10 0]);
        figure
        plot(t,xa(:,1),t,xa(:,2),t,xa(:,3))
        title(['Viral Spread of Infection'])
        xlabel('t (days)')
        ylabel('Population')
        legend('S','I','R')
    end
end
This incorporates ‘q’ into your epidemiology model.
I leave it to you to determine if this is the best option for your homework problem.
EDIT — For what it’s worth, ‘qI’ will throw an error because it is an undefined variable. You likely want ‘q*I’, since MATLAB does not recognise implied multiplication. Of course, we still have to know what ‘I’ is.
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